CN111644909B - Method for solving grinding track of rear cutter face of woodworking forming milling cutter - Google Patents
Method for solving grinding track of rear cutter face of woodworking forming milling cutter Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B3/00—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools
- B24B3/02—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools of milling cutters
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Abstract
The invention discloses a method for solving a grinding track of a rear cutter face of a woodworking forming milling cutter. The invention deals with the flexible and changeable irregular edge line of the forming edge by the flexible grinding attitude of the grinding wheel, and can realize the flexibility of the definition of the grinding attitude of the grinding wheel by judging the position of the grinding point while ensuring the grinding quality, thereby ensuring the accurate clearance angle and avoiding interference.
Description
Technical Field
The invention belongs to the technical field of woodworking forming milling cutters, and particularly relates to a method for solving a grinding track of a rear cutter face of a woodworking forming milling cutter.
Background
With the development of the woodworking tool market, higher requirements are put forward on the research and development direction research of the woodworking tool. The forming mode of the wood milling cutter is similar to that of a metal milling cutter, but compared with the metal milling cutter, the wood milling cutter has the characteristics of large front angle, large back angle, few cutting teeth, large length and shape span of a cutting edge and the like. The existing research on the grinding track of the related metal milling cutter can not be directly applied to a woodworking milling cutter. Therefore, research is carried out aiming at the grinding method of the rear cutter face of the woodworking forming milling cutter, and the method has very important significance for improving the grinding precision of the woodworking forming milling cutter.
The forming principle of the woodworking milling cutter is the same as that of a metal cutting milling cutter, and is also the forming principle of a generating method. The profile shape depends on the axial cross-sectional shape of the cutting edge's profile of revolution, rather than the actual shape of each tooth of the tool. Therefore, how to convert the complex rotary shape of the cutter into the rotary contour shaft section shape of the cutting edge; how to mathematically express the motion trail of the grinding wheel in the cutter sharpening process; and how to convert the tool position track of the grinding wheel for tool sharpening to the motion of each shaft of a specific numerical control machine tool becomes a key problem for researching the method for sharpening the woodworking milling cutter. The woodworking forming milling cutter has the advantages of flexible and complex forming shape, stable cutting performance, high durability and high cutting speed, but has a plurality of difficulties in the manufacturing process: the grinding amount is large, the shape fall is large, and a non-orthogonal edge line and the like are generated in the process of processing a blank to a finished product. Therefore, an accurate grinding method capable of avoiding interference is urgently needed to improve the manufacturing precision of the rear cutter face of the woodworking forming milling cutter and reduce the grinding preparation difficulty of the rear cutter face.
Disclosure of Invention
The invention aims to provide a grinding process for machining a rear cutter face of a woodworking milling cutter, aiming at machining the woodworking milling cutter with non-orthogonal cutting edges, ensuring the grinding quality and realizing the flexibility of definition of the grinding attitude of a grinding wheel through different rear angle orientations and other process parameters so as to avoid interference.
The invention discloses a method for solving a grinding track of a rear cutter face of a woodworking forming milling cutter, which comprises the following steps:
step 1: defining geometrical parameters relating to the shaped edge
(1) Eccentricity value H: and defining the distance between the plane of the forming edge and the rotary central plane of the cutter as an eccentricity value H.
(2) Point P on the revolving contour axis sectional shape of the cutting edge: woodworking milling cutters are generally known as the shape of revolution of a blade, defining the point on the profile axis cross-sectional shape of the revolution of the shaped blade as point P.
(3) Grinding point P0: defining the grinding point on the cutting edge under the coordinate system of the workpiece as P0And (4) point.
(4) Grinding point P on the end of the flank face0Corresponding point P1: over grinding point P0Making a plane vertical to the rear cutter face, and the intersection point of the plane and the rear cutter face end is P1And (4) point.
Step 2: defining a coordinate system
(1) Workpiece coordinate system Ow-XwYwZw: in order to facilitate the cutter setting of the numerical control grinding of the woodworking forming milling cutter and obtain an NC program for controlling a machine tool, a point P on the section shape of a rotating contour shaft of the cutter needs to be converted into the actual coordinate of a forming edge under a workpiece coordinate system for carrying outA description is given. Defining the tool rotation axis as ZwThe shaft takes the end face where the start point of the woodworking milling cutter forming edge is positioned as XwOwYwPlane of origin of coordinates OwThe connecting line of the forming edge line starting point and the forming edge line is X of a workpiece coordinate systemwA shaft.
(2) Cutting edge coordinate system Om-XmYmZm: the cutting edge coordinate system is a floating coordinate system, and the origin of the coordinate system is positioned at the grinding point P0At least one of (1) and (b); edge line is on P0The tangent vector of the point is defined as Z of the cutting edge coordinate systemmAxis, XmAxis parallel to XwA shaft.
Point P from coordinate P in cutting edge coordinate systemmCoordinate P converted into workpiece coordinate systemwIs shown in formula (1)
Pw＝Mm-w·Pm+Tm-w (1)
In the formula Mm-wA rotation matrix representing the coordinate system of the cutting edge to the coordinate system of the workpiece:
wherein θ is ZmAxis and ZwThe included angle between the axes; in the cutting edge coordinate system, let Ph(xph_w、yph_w、zph_w) To and from the grinding point P0(xp0_w、yp0_w、zp0_w) Adjacent edge line coordinate points, then θ is expressed as follows:
Tm-wa translation matrix representing the coordinate system of the cutting edge to the coordinate system of the workpiece:
and step 3: definition of formed edge and rear face of woodworking milling cutter
(1) Width and clearance angle of the flank face of the formed blade: all definitions of the rear cutter face of the formed blade of the woodworking milling cutter are based on a cutting edge coordinate system; the width and the clearance angle of the flank of the forming edge are XmYmThe plane is used as a reference.
Definition P0P1Is the flank face and XmYmThe intersection line of the planes, i is the width of the first rear cutter face; λ is the first relief angle.
P0The coordinate of the point in the cutting edge coordinate system is P0_m(0,0,0), P is found by analysis1Point coordinate P1_mThe coordinates in the cutting edge coordinate system are expressed as follows:
(2) normal vector of flank face of formed edge
Defining the unit normal vector of the flank face of the formed edge as Fg0_mThe expression of which in the cutting edge coordinate system is as follows:
and 4, step 4: grinding wheel trajectory calculation
(1) Initial attitude of grinding wheel
In order to ensure the grinding quality of the rear cutter face of the formed blade of the woodworking cutter, a grinding mode of flexibly adjusting the posture of the grinding wheel according to different relief angle directions corresponding to different grinding points on a blade line is adopted to define Fy_mIs the Y of the coordinate system of the workpiecewThe expression of the axis in the cutting-edge coordinate system, i.e.
Definition P0Point of direction P1Vector of (a) is FtThen F istPerpendicular FyAnd F istAnd FyFormed flatThe surface is superposed with the grinding wheel end surface under the initial posture of the grinding wheel; the normal vector defining the plane is the grinding wheel axis vector FgExpressed as
Fg_m＝Ft_m×Fy_m (8)
Definition P0Point to the center point O of grinding end face circle of grinding wheelgI.e. the vector of the tool location point is FbThe big end face of the grinding wheel is P0Point and vector FtTangency; due to FbPerpendicular to FgAnd FtThen, in the cutting edge coordinate system
Fb_m＝Fg_m×Ft_m (9)
Therefore, only need to put P0Along vector FbRadius R of end face of grinding wheel moved in directiongThe expression of the tool location point coordinates in the cutting edge coordinate system can be obtained:
Og_m＝P0_m+Rg_m·Fb_m (10)
(2) influence of grinding wheel swing angle technological parameters on initial attitude
In order to avoid interference between the grinding wheel and other characteristic structures of the formed edge possibly generated in the grinding process of the rear tool face, introducing a grinding wheel swing angle process parameter into a cutting edge coordinate system; defining the profile edge flank face at P0Normal vector at point is Fg0Expressed as
Define the swing angle muagFor grinding wheel with P0Centered on vector Fg0The angle of rotation of the rotating shaft.
Any unit vector N (N) around the space is knownx,Ny,Nz) The rotation matrix Rot rotated by an angle γ has the general formula:
wherein vers γ is 1-cos γ.
Then point P1Around vector Fg0Angle of rotation muαgObtain a point P1', the expression thereof is as follows:
P1′＝Rot(Fg0_m,μαg)P1_m (13)
from point P1' and Point P0Obtain a vector Ft' according to the expressions (8) to (10), a grinding wheel spindle vector F having a swing angle is estimatedg' and tool location point coordinate O with swing angleg'。
(3) Influence of grinding wheel angle lifting process parameters on initial attitude
In order to reduce the grinding contact area between the grinding wheel and the rear cutter face in the grinding process of the rear cutter face, introducing a lifting angle process parameter of the grinding wheel into a cutting edge coordinate system; defining the lift angle deltaαgGrinding wheel axis vector F with swing angle for grinding wheel after swing angle conversiont' angle of rotation.
Definition F in the cutting edge coordinate systemg"is the grinding wheel axis vector converted by raising angle, which is represented by Fg' winding Ft' rotation deltaαgTo obtain
F″g_m＝Rot(F′t_m,δαg)F′g_m (14)
Further according to the formulas (8) to (10), the grinding wheel cutter position point coordinate O with the lifting angle is calculated and obtainedg”。
(4) Description of grinding wheel trajectory in workpiece coordinate system
The grinding point P which is obtained by the transformation and has floating combination of the tool location point coordinate and the sand wheel axis vector0Obtaining any point P of the formed blade of the woodworking milling cutter0Corresponding knife location point coordinates and a sand wheel shaft vector; the grinding wheel axis vector and the tool location point coordinate are described in a cutting edge coordinate system, and in order to be used for actual processing, the grinding wheel axis vector and the tool location point coordinate need to be finally converted into a workpiece coordinate system for expression; the transformation matrix is shown in formulas (15) and (16), wherein Og_wAs a coordinate of the location of the knife point, Fg_wAs the grinding wheel axis vector:
Fg_w＝Mm-w·F″g_m (15)
Og_w＝Mm-w·O″g_m+Tm-w (16)
the invention has the beneficial effects that:
the invention defines the grinding wheel posture for grinding the rear cutter face of the formed cutter edge of the woodworking milling cutter, and provides a grinding track algorithm for the rear cutter face of the formed cutter edge of the woodworking milling cutter based on a non-orthogonal formed cutter edge line with technological parameters such as tooth offset value and the like. The algorithm deals with the flexible and changeable irregular edge lines of the formed edge by the flexible grinding attitude of the grinding wheel, and can realize the flexibility of the definition of the grinding attitude of the grinding wheel by judging the position of a grinding point while ensuring the grinding quality, thereby ensuring the accuracy of a back angle and avoiding interference.
Drawings
FIG. 1 is a schematic sectional view of a profiled blade revolution profile shaft.
Fig. 2 is a schematic diagram of the positions of the cutting edge coordinate system and the workpiece coordinate system.
Fig. 3 is a schematic view of a profiled edge relief.
Fig. 4 is a schematic diagram of the change of the swing angle of the grinding wheel.
FIG. 5 is a schematic view of the change of the lifting angle of the grinding wheel.
Fig. 6 is a graph showing the simulation result of grinding the flank face of the formed edge of the woodworking milling cutter.
Fig. 7 is an actual grinding process.
Fig. 8 shows the actual grinding to obtain the formed blade of the woodworking milling cutter.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
Step 1: defining the geometric parameters of the formed edge of the woodworking milling cutter
(1) Eccentricity value H: the distance between the plane of the forming edge and the rotary central plane of the cutter is defined as H.
(2) Point P on the revolving contour axis sectional shape of the cutting edge: woodworking milling cutters are generally known as the shape of revolution of a blade, defining the point on the profile axis cross-sectional shape of the revolution of the shaped blade as point P.
(3) Grinding point P0: defining the grinding point on the cutting edge under the coordinate system of the workpiece as P0And (4) point.
(4) Grinding point P on the end of the flank face0Corresponding point P1: over grinding point P0Making a plane vertical to the rear cutter face, and the intersection point of the plane and the rear cutter face end is P1And (4) point.
Step 2: defining coordinate system definitions
(1) Workpiece coordinate system Ow-XwYwZw: in order to facilitate the tool setting of the numerical control grinding of the woodworking forming milling cutter and obtain an NC program for controlling a machine tool, a point P on the section shape of a tool rotating contour shaft needs to be converted into the coordinate of the actual forming edge under a workpiece coordinate system for description. Defining the tool rotation axis as ZwThe shaft takes the end face where the start point of the woodworking milling cutter forming edge is positioned as XwOwYwPlane of origin of coordinates OwThe connecting line of the forming edge line starting point and the forming edge line is X of a workpiece coordinate systemwA shaft.
(2) Cutting edge coordinate system Om-XmYmZm: the cutting edge coordinate system is a floating coordinate system, and the origin of the coordinate system is positioned at the grinding point P0To (3). Edge line is on P0The tangent vector of the point is defined as Z of the cutting edge coordinate systemmAxis, XmAxis parallel to XwA shaft.
Point P from coordinate P in cutting edge coordinate systemmCoordinate P converted into workpiece coordinate systemwIs shown as equation (17)
Pw＝Mm-w·Pm+Tm-w (17)
In the formula Mm-wA rotation matrix representing the coordinate system of the cutting edge to the coordinate system of the workpiece:
wherein θ is ZmAxis and ZwThe angle between the axes. Setting a point P under the cutting edge coordinate systemh(xph_w、yph_w、zph_w) Is composed ofAnd grinding point P0(xp0_w、yp0_w、zp0_w) Adjacent edge line coordinate points, then θ is expressed as follows:
Tm-wa translation matrix representing the translation from the end-tooth coordinate system to the workpiece coordinate system:
and step 3: definition of formed edge and rear face of woodworking milling cutter
(3) Width and clearance angle of the flank face of the formed blade: in the present invention, all definitions of the formed edge flank of the woodworking milling cutter are based on the cutting edge coordinate system. The width and the clearance angle of the flank of the forming edge are XmYmThe plane is used as a reference.
Definition P0P1Is the flank face and XmYmThe intersection line of the planes, i is the width of the first rear cutter face; λ is the first relief angle.
P0The coordinate of the point in the cutting edge coordinate system is P0_m(0,0,0), then P can be known from the geometrical relationship shown1Point coordinate P1_mCan be expressed as follows:
(4) normal vector of flank face of formed edge
Defining the unit normal vector of the flank face of the formed edge as Fg0The expression of which in the cutting edge coordinate system is as follows:
and 4, step 4: grinding wheel trajectory calculation
(1) Initial attitude of grinding wheel
In order to ensure the grinding quality of the rear cutter face of the formed blade of the woodworking cutter, a grinding mode of flexibly adjusting the posture of the grinding wheel according to different relief angle directions corresponding to different grinding points on a blade line is adopted. Definition FyIs the Y of the coordinate system of the workpiecewExpression of the axis in the cutting edge coordinate system. Namely, it is
Definition P0Point of direction P1Vector of (a) is FtThen F istPerpendicular FyAnd F istAnd FyThe plane formed coincides with the grinding wheel end face in the initial posture of the grinding wheel. The normal vector defining the plane is the grinding wheel axis vector FgThen, in the cutting edge coordinate system, can be expressed as
Fg_m＝Ft_m×Fy_m (24)
Definition P0Point to the center point O of grinding end face circle of grinding wheelg(the tool position point) vector is FbThe big end face of the grinding wheel is P0Point and vector FtTangent. Due to FbPerpendicular to FgAnd FtThen, it can be obtained under the cutting edge coordinate system
Fb_m＝Fg_m×Ft_m (25)
Therefore, only need to put P0Along vector FbRadius R of end face of grinding wheel moved in directiongThe expression of the tool location point coordinates in the cutting edge coordinate system can be obtained:
Og_m＝P0_m+Rg_m·Fb_m (26)
(2) influence of grinding wheel swing angle technological parameters on initial attitude
In order to avoid interference between the grinding wheel and other characteristic structures of the formed edge, which can be generated in the grinding process of the flank face, a grinding wheel swing angle process parameter is introduced into a cutting edge coordinate system. Defining the profile edge flank face at P0Normal vector at point is Fg0Then, in the cutting edge coordinate system, can be expressed as
Define the swing angle muagFor grinding wheel with P0Centered on vector Fg0The angle of rotation of the rotating shaft.
Any unit vector N (N) around the space is knownx,Ny,Nz) The rotation matrix Rot rotated by an angle γ has the general formula:
wherein vers γ is 1-cos γ.
Then point P1Around vector Fg0Angle of rotation muαgObtain a point P1', the expression thereof is as follows:
P1′＝Rot(Fg0_m,μαg)P1_m (29)
from point P1' and Point P0Obtain a vector Ft', according to the expressions (8) to (10), the grinding wheel axial vector F having the swing angle can be estimatedg' and tool location point coordinate Og'。
(3) Influence of grinding wheel angle lifting process parameters on initial attitude
In order to reduce the grinding contact area between the grinding wheel and the rear tool face in the grinding process of the rear tool face, angle raising technological parameters of the grinding wheel are introduced into a cutting edge coordinate system. Defining the lift angle deltaαgVector F after the grinding wheel is subjected to swing angle conversiont' angle of rotation.
Definition F in the cutting edge coordinate systemg"is the grinding wheel axis vector converted by raising angle, which can be represented by Fg' winding Ft' rotation deltaαgTo obtain
F″g_m＝Rot(F′t_m,δαg)F′g_m (30)
Further according to the formulas (8) to (10), the grinding wheel cutter position point coordinate O with the lifting angle can be calculatedg”。
(4) Description of grinding wheel trajectory in workpiece coordinate system
The grinding point P which is obtained by the transformation and has floating combination of the tool location point coordinate and the sand wheel axis vector0The coordinate of the cutter can obtain the arbitrary point P of the forming edge of the woodworking milling cutter0The corresponding tool location point coordinates and the sand wheel axis vector. And the grinding wheel axis vector and the tool location point coordinate are described in the cutting edge coordinate system, so that the grinding wheel axis vector and the tool location point coordinate are required to be finally converted into a workpiece coordinate system for expression in order to be used for actual machining. The transformation matrix is shown in formulas (31), (32), wherein Og_wAs a coordinate of the location of the knife point, Fg_wAs the grinding wheel axis vector:
Fg_w＝Mm-w·F″g_m (31)
Og_w＝Mm-w·O″g_m+Tm-w (32)
based on the grinding track algorithm provided by the invention, a set of algorithm modules are developed by utilizing VC + + environment, and after relevant process parameters are input, the grinding wheel grinding numerical control program corresponding to the theoretical forming edge line can be obtained by circularly calculating according to a certain step length. And importing an NC program into Vericut simulation software, carrying out grinding simulation and checking the interference condition. The simulation result of the grinding of the rear face of the formed edge of the woodworking milling cutter is shown in fig. 6.
The actual grinding process is shown in FIG. 7, the grinding wheel speed is 25m/s, the feed speed is 10mm/s, and the grinding process adopts grinding oil for cooling.
Grinding the woodworking milling cutter under the condition of keeping the same technological parameters and numerical control programs, and observing the geometric parameters of the ground formed milling cutter by using a cutter detector PG-1000 respectively, wherein the error of the cutter parameters is within 3 percent, and the cutter parameters have higher goodness of fit with the design values.
Claims (1)
1. A method for solving the grinding track of the rear cutter face of a woodworking forming milling cutter is characterized by comprising the following steps:
step 1: defining geometrical parameters relating to the shaped edge
(1) Eccentricity value H: defining the distance between the plane of the forming edge and the rotary central plane of the cutter as an eccentricity value H;
(2) point P on the revolving contour axis sectional shape of the cutting edge: the woodworking forming milling cutter is a rotary shape of a known blade, and a point on the section shape of a rotary profile shaft of a forming blade is defined as a point P;
(3) grinding point P0: defining the grinding point on the cutting edge under the coordinate system of the workpiece as P0Point;
(4) grinding point P on the end of the flank face0Corresponding point P1: over grinding point P0Making a plane vertical to the rear cutter face, and the intersection point of the plane and the rear cutter face end is P1Point;
step 2: defining a coordinate system
(1) Workpiece coordinate system Ow-XwYwZw: in order to facilitate the cutter setting of the numerical control grinding of the woodworking forming milling cutter and obtain an NC program for controlling a machine tool, a point P on the section shape of a rotary contour shaft of the cutter needs to be converted into a coordinate where a forming edge is actually located under a workpiece coordinate system for description; defining the tool rotation axis as ZwThe shaft takes the end face where the start point of the woodworking milling cutter forming edge is positioned as XwOwYwPlane of origin of coordinates OwThe connecting line of the forming edge line starting point and the forming edge line is X of a workpiece coordinate systemwA shaft;
(2) cutting edge coordinate system Om-XmYmZm: the cutting edge coordinate system is a floating coordinate system, and the origin of the coordinate system is positioned at the grinding point P0At least one of (1) and (b); edge line is on P0The tangent vector of the point is defined as Z of the cutting edge coordinate systemmAxis, XmAxis parallel to XwA shaft;
point P from coordinate P in cutting edge coordinate systemmCoordinate P converted into workpiece coordinate systemwIs shown in formula (1)
Pw＝Mm-w·Pm+Tm-w (1)
In the formula Mm-wA rotation matrix representing the coordinate system of the cutting edge to the coordinate system of the workpiece:
wherein θ is ZmAxis and ZwThe included angle between the axes; in the cutting edge coordinate system, let Ph(xph_w、yph_w、zph_w) To and from the grinding point P0(xp0_w、yp0_w、zp0_w) Adjacent edge line coordinate points, then θ is expressed as follows:
Tm-wa translation matrix representing the coordinate system of the cutting edge to the coordinate system of the workpiece:
and step 3: definition of formed edge and rear face of woodworking milling cutter
(1) Width and clearance angle of the flank face of the formed blade: all definitions of the rear cutter face of the formed blade of the woodworking milling cutter are based on a cutting edge coordinate system; the width and the clearance angle of the flank of the forming edge are XmYmThe plane is taken as a reference;
definition P0P1Is the flank face and XmYmThe intersection line of the planes, i is the width of the first rear cutter face; λ is a first relief angle;
P0the coordinate of the point in the cutting edge coordinate system is P0_m(0,0,0), P is found by analysis1Point coordinate P1_mThe coordinates in the cutting edge coordinate system are expressed as follows:
(2) normal vector of flank face of formed edge
Defining the unit normal vector of the flank face of the formed edge as Fg0_mThe expression of which in the cutting edge coordinate system is as follows:
and 4, step 4: grinding wheel trajectory calculation
(1) Initial attitude of grinding wheel
In order to ensure the grinding quality of the rear cutter face of the formed blade of the woodworking cutter, a grinding mode of flexibly adjusting the posture of the grinding wheel according to different relief angle directions corresponding to different grinding points on a blade line is adopted to define Fy_mIs the Y of the coordinate system of the workpiecewThe expression of the axis in the cutting-edge coordinate system, i.e.
Definition P0Point of direction P1Vector of (a) is FtThen F istPerpendicular FyAnd F istAnd FyThe formed plane is superposed with the grinding wheel end face under the initial posture of the grinding wheel; the normal vector defining the plane is the grinding wheel axis vector FgExpressed as
Fg_m＝Ft_m×Fy_m (8)
Definition P0Point to the center point O of grinding end face circle of grinding wheelgI.e. the vector of the tool location point is FbThe big end face of the grinding wheel is P0Point and vector FtTangency; due to FbPerpendicular to FgAnd FtThen, in the cutting edge coordinate system
Fb_m＝Fg_m×Ft_m (9)
Therefore, only need to put P0Along vector FbRadius R of end face of grinding wheel moved in directiongThe expression of the tool location point coordinates in the cutting edge coordinate system can be obtained:
Og_m＝P0_m+Rg_m·Fb_m (10)
(2) influence of grinding wheel swing angle technological parameters on initial attitude
In order to avoid interference between the grinding wheel and other characteristic structures of the formed edge possibly generated in the grinding process of the rear tool face, introducing a grinding wheel swing angle process parameter into a cutting edge coordinate system; defining the profile edge flank face at P0Normal vector at point is Fg0Expressed as
Define the swing angle muagFor grinding wheel with P0Centered on vector Fg0The angle of rotation of the rotating shaft;
any unit vector N (N) around the space is knownx,Ny,Nz) The rotation matrix Rot rotated by an angle γ has the general formula:
wherein vers γ is 1-cos γ;
then point P1Around vector Fg0Angle of rotation muαgObtain a point P1', the expression thereof is as follows:
P1′＝Rot(Fg0_m,μαg)P1_m (13)
from point P1' and Point P0Obtain a vector Ft' according to the expressions (8) to (10), a grinding wheel spindle vector F having a swing angle is estimatedg' and tool location point coordinate O with swing angleg'；
(3) Influence of grinding wheel angle lifting process parameters on initial attitude
In order to reduce the grinding contact area between the grinding wheel and the rear cutter face in the grinding process of the rear cutter face, introducing a lifting angle process parameter of the grinding wheel into a cutting edge coordinate system; defining the lift angle deltaαgA grinding wheel shaft vector F 'with a swing angle after the grinding wheel is wound by the swing angle conversion'tThe angle of rotation;
definition F in the cutting edge coordinate systemgIs changed by raising angleGrinding wheel axis vector ofg' winding Ft' rotation deltaαgTo obtain
F″g_m＝Rot(F′t_m,δαg)F′g_m (14)
Further according to the formulas (8) to (10), the grinding wheel cutter position point coordinate O with the lifting angle is calculated and obtainedg”；
(4) Description of grinding wheel trajectory in workpiece coordinate system
The grinding point P which is obtained by the transformation and has floating combination of the tool location point coordinate and the sand wheel axis vector0Obtaining any point P of the formed blade of the woodworking milling cutter0Corresponding knife location point coordinates and a sand wheel shaft vector; the grinding wheel axis vector and the tool location point coordinate are described in a cutting edge coordinate system, and in order to be used for actual processing, the grinding wheel axis vector and the tool location point coordinate need to be finally converted into a workpiece coordinate system for expression; the transformation matrix is shown in formulas (15) and (16), wherein Og_wAs a coordinate of the location of the knife point, Fg_wAs the grinding wheel axis vector:
Fg_w＝Mm-w·F″g_m (15)
Og_w＝Mm-w·O″g_m+Tm-w (16)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010452412.4A CN111644909B (en) | 2020-05-26 | 2020-05-26 | Method for solving grinding track of rear cutter face of woodworking forming milling cutter |
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| CN202010452412.4A CN111644909B (en) | 2020-05-26 | 2020-05-26 | Method for solving grinding track of rear cutter face of woodworking forming milling cutter |
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| CN112222959B (en) * | 2020-10-13 | 2021-08-03 | 西南交通大学 | Grinding wheel wear parameter-based grinding track compensation method for rear cutter face of end mill |
| CN112989517B (en) * | 2021-03-16 | 2022-06-24 | 西南交通大学 | Method for solving track of grinding rear cutter face of ball head by adopting parallel grinding wheel |
| CN113255075A (en) * | 2021-05-26 | 2021-08-13 | 西南交通大学 | Grinding track algorithm for rear tool face of chip-breaking drill tip |
| CN113868805A (en) * | 2021-10-22 | 2021-12-31 | 西南交通大学 | Method for calculating grinding track of rear tool face of straight edge of drill tip |
| CN114918747A (en) * | 2022-05-17 | 2022-08-19 | 深圳数马电子技术有限公司 | Method and device for grinding rear face of three-face edge milling cutter and computer equipment |
| CN114850977B (en) * | 2022-05-31 | 2023-05-05 | 西南交通大学 | Grinding track solving method for processing noncircular irregular shaft by adopting segment difference grinding process |
| CN115446674A (en) * | 2022-09-08 | 2022-12-09 | 深圳数马电子技术有限公司 | Grinding method and device for rear cutter face of inner R milling cutter, numerical control machine and storage medium |
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